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TITLE: General Inversion of Phase Technique (GIPhT)

OVERVIEW: Synthetic aperture radar (SAR) is an active remote sensing technique used for measuring geophysical activity on the Earth’s surface. It records microwaves transmitted by a sensor (usually aboard a satellite) and reflected by features on the Earth’s surface (usually on land). The reflected signal contains information in the form of amplitude and phase data, and requires sophisticated post-processing. A technique known as interferometric SAR (InSAR) measures the difference in phase between two images of the same area, which can be used to measure motion and deformation of the ground. In most applications, the interferogram must be “unwrapped” before it can be interpreted. The unwrapped interferogram may be used to monitor geophysical changes on the Earth’s surface associated with earthquakes, volcanoes, landslides or glaciers, or with the withdrawal of oil, gas, water or minerals by extractive industries. Unwrapping requires considerable computational power and time, and may lead to significant mistakes in the unwrapped interferogram and thus in its intepretation. UW-Madison researchers have developed an algorithm for interpreting an interferogram without the need for unwrapping. To do so, the invention interprets the interferogram by estimating parameters in a quantitative model directly from the wrapped phase data. Alternative unwrapping algorithms have been developed, but these can provide inadequate results in areas where the phase data are imperfect, leading to errors in the unwrapped phase values. Likewise, these algorithms rarely, if ever, provide uncertainty estimates, limiting attempts to weight the data in statistical analysis. Implementation of the invention would reduce the time and resources necessary for advanced interpretation of InSAR data products, and would provide a more accurate result that includes an assessment of the uncertainties of the parameter estimates.

APPLICATIONS: InSAR for monitoring hazardous natural phenomena, e.g., landslides InSAR for monitoring subsidence due to extraction, e.g., oil, gas, water KEY

BENEFITS: Validated on real (noisy) data in a peer-reviewed publication Provides a more direct path to a quantitative interpretation than existing methods Provides a realistic assessment of uncertainty, unlike existing methods

PUBLICATIONS: Feigl, K. L., and C. H. Thurber (2009) A method for modelling radar interferograms without phase unwrapping: application to the M 5 Fawnskin, California earthquake of 1992 December 4 Geophys. J. Int., 176, 491-504. http://dx.doi.org/10.1111/j.1365-246X.2008.03881.x
Interferometric analysis of synthetic aperture radar images (InSAR) measures the phase shifts between two images acquired at two distinct times. These ambiguous 'wrapped' phase values range from -1/2 to +1/2 cycles. The standard approach interprets the phase values in terms of the change in distance between the ground and the radar instrument by resolving the integer ambiguities in a process known as 'unwrapping'. To avoid unwrapping, we have developed, validated and applied a new method for modelling the wrapped phase data directly. The method defines a cost function in terms of wrapped phase to measure the misfit between the observed and modelled values of phase. By minimizing the cost function with a simulated annealing algorithm, the method estimates parameters in a non-linear model. Since the wrapped phase residuals are compatible with a von Mises distribution, several parametric statistical tests can be used to evaluate the fit of the model to the data. The method, named General Inversion for Phase Technique (GIPhT), can handle noisy, wrapped phase data. Applying GIPhT to two interferograms in the area of Fawnskin, California, we estimate a set of model parameters describing a magnitude 5 aftershock of the 1992 Landers earthquake. The resulting simulation fits the data well. The phase final residuals have a circular mean deviation less than 0.15 cycles per datum. Sampling the final residuals, we find the circular standard deviation of a phase measurement to be approximately 0.2 cycle, corresponding to 6 mm in range.

EXAMPLES:

https://uwmadison.box.com/s/a6nlx7q803uyfaog64r25ulnlb1nr52i

LICENSING:

Copyright (c) Kurt Feigl, Cliff Thurber, Lee Powell, Peter Sobol, Aaron Masters, S. Tabrez Ali, Elena C. Reinisch, University of Wisconsin-Madison

This program is free software: you can redistribute it and/or modify it under the terms of the GNU LESSER GENERAL PUBLIC LICENSE as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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